Block operations for an image processor having a two-dimensional execution lane array and a two-dimensional shift register

ABSTRACT

A method is described that includes, on an image processor having a two dimensional execution lane array and a two dimensional shift register array, repeatedly shifting first content of multiple rows or columns of the two dimensional shift register array and repeatedly executing at least one instruction between shifts that operates on the shifted first content and/or second content that is resident in respective locations of the two dimensional shift register array that the shifted first content has been shifted into.

FIELD OF INVENTION

The field of invention pertains generally to image processing, and, morespecifically, to block operations for an image processor having atwo-dimensional execution lane array and a two-dimensional shiftregister.

BACKGROUND

Image processing typically involves the processing of pixel values thatare organized into an array. Here, a spatially organized two dimensionalarray captures the two dimensional nature of images (additionaldimensions may include time (e.g., a sequence of two dimensional images)and data type (e.g., colors). In a typical scenario, the arrayed pixelvalues are provided by a camera that has generated a still image or asequence of frames to capture images of motion. Traditional imageprocessors typically fall on either side of two extremes.

A first extreme performs image processing tasks as software programsexecuting on a general purpose processor or general purpose-likeprocessor (e.g., a general purpose processor with vector instructionenhancements). Although the first extreme typically provides a highlyversatile application software development platform, its use of finergrained data structures combined with the associated overhead (e.g.,instruction fetch and decode, handling of on-chip and off-chip data,speculative execution) ultimately results in larger amounts of energybeing consumed per unit of data during execution of the program code.

A second, opposite extreme applies fixed function hardwired circuitry tomuch larger blocks of data. The use of larger (as opposed to finergrained) blocks of data applied directly to custom designed circuitsgreatly reduces power consumption per unit of data. However, the use ofcustom designed fixed function circuitry generally results in a limitedset of tasks that the processor is able to perform. As such, the widelyversatile programming environment (that is associated with the firstextreme) is lacking in the second extreme.

A technology platform that provides for both highly versatileapplication software development opportunities combined with improvedpower efficiency per unit of data remains a desirable yet missingsolution.

SUMMARY

A method is described that includes, on an image processor having a twodimensional execution lane array and a two dimensional shift registerarray, repeatedly shifting first content of multiple rows or columns ofthe two dimensional shift register array and repeatedly executing atleast one instruction between shifts that operates on the shifted firstcontent and/or second content that is resident in respective locationsof the two dimensional shift register array that the shifted firstcontent has been shifted into.

An apparatus is described that includes means for, on an image processorhaving a two dimensional execution lane array and a two dimensionalshift register array, repeatedly shifting first content of multiple rowsor columns of the two dimensional shift register array and repeatedlyexecuting at least one instruction between shifts that operates on theshifted first content and/or second content that is resident inrespective locations of the two dimensional shift register array thatthe shifted first content has been shifted into.

LIST OF FIGURES

The following description and accompanying drawings are used toillustrate various embodiments of the invention. In the drawings:

FIG. 1 shows various components of a technology platform;

FIG. 2a shows an embodiment of application software built with kernels;

FIG. 2b shows an embodiment of the structure of a kernel;

FIG. 3 shows an embodiment of the operation of a kernel;

FIGS. 4a, 4b and 4c depict various aspects of a virtual processor'smemory model for developing kernel threads in a higher level applicationsoftware development environment;

FIG. 5a shows an embodiment of a thread written with load instructionshaving a position relative format;

FIG. 5b shows images having different pixel densities;

FIG. 6 shows an embodiment of an application software development andsimulation environment;

FIG. 7 shows an embodiment of an image processor hardware architecture;

FIGS. 8a, 8b, 8c, 8d and 8e depict the parsing of image data into a linegroup, the parsing of a line group into a sheet and the operationperformed on a sheet with overlapping stencils;

FIG. 9a shows an embodiment of a stencil processor;

FIG. 9b shows an embodiment of a instruction word of the stencilprocessor;

FIG. 10 shows an embodiment of a data computation unit within a stencilprocessor;

FIGS. 11a, 11b, 11c, 11d, 11e , 111, 11 g, 11 h, 11 i, 11 j and 11 kdepict an example of the use of a two-dimensional shift array and anexecution lane array to determine a pair of neighboring output pixelvalues with overlapping stencils;

FIG. 12 shows an embodiment of a unit cell for an integrated executionlane array and two-dimensional shift array;

FIG. 13 shows a two-dimensional row/column sum operation;

FIGS. 14a, 14b, 14c and 14d show low level operations for implementing atwo dimensional row sum operation;

FIG. 15 pertains to a two-dimensional prefix sum operation;

FIGS. 16a, 16b, 16c and 16d show low level operations for implementing atwo-dimensional prefix sum operation;

FIG. 17 pertains to a two-dimensional find minimum operation;

FIGS. 18a, 18b, 18c and 18d show low level operations for implementing atwo-dimensional find minimum operation;

FIGS. 19a and 19b show a matrix multiply operation;

FIGS. 20a, 20b, 20c, 20d and 20e show low level operations forimplementing a matrix multiply operation with a two dimensional shiftregister;

FIG. 21 shows a DFT operation;

FIGS. 22a, 22b, 22c, 22d, 22e and 22f show low level operations forimplementing a DFT operation with a two dimensional shift register;

FIG. 23 shows butterfly operations;

FIGS. 24a, 24b and 24c show butterfly operations implemented with atwo-dimensional shift register;

FIG. 25 shows a base image and an alternative image having a blockimage;

FIGS. 26a, 26b, 26c and 26d show low level operations for performing ablock matching algorithm;

FIG. 27 shows an environment for generating program code that istargeted to a hardware platform having a two-dimensional execution lanearray and a two-dimensional shift register array;

FIG. 28 shows an embodiment of a computing system.

DETAILED DESCRIPTION

i. Introduction

The description below describes numerous embodiments concerning a newimage processing technology platform that provides a widely versatileapplication software development environment that uses larger blocks ofdata (e.g., line groups and sheets as described further below) toprovide for improved power efficiency.

1.0 Application Software Development Environment

a. Application and Structure of Kernels

FIG. 1 shows a high level view of an image processor technology platformthat includes a virtual image processing environment 101, the actualimage processing hardware 103 and a compiler 102 for translating higherlevel code written for the virtual processing environment 101 to objectcode that the actual hardware 103 physically executes. As described inmore detail below, the virtual processing environment 101 is widelyversatile in terms of the applications that can be developed and istailored for easy visualization of an application's constituentprocesses. Upon completion of the program code development effort by thedeveloper 104, the compiler 102 translates the code that was writtenwithin the virtual processing environment 101 into object code that istargeted for the actual hardware 103.

FIG. 2a shows an example of the structure and form that applicationsoftware written within the virtual environment may take. As observed inFIG. 2a , the program code may be expected to process one or more framesof input image data 201 to effect some overall transformation on theinput image data 201. The transformation is realized with the operationof one or more kernels of program code 202 that operate on the inputimage data in an orchestrated sequence articulated by the developer.

For example, as observed in FIG. 2a , the overall transformation iseffected by first processing each input image with a first kernel K1.The output images produced by kernel K1 are then operated on by kernelK2. Each of the output images produced by kernel K2 are then operated onby kernel K3_1 or K3_2. The output images produced by kernel(s)K3_1/K3_2 are then operated on by kernel K4. Kernels K3_1 and K3_2 maybe identical kernels designed to speed-up the overall processing byimposing parallel processing at the K3 stage, or, may be differentkernels (e.g., kernel K3_1 operates on input images of a first specifictype and kernel K3_2 operates on input images of a second, differenttype).

As such, the larger overall image processing sequence may take the formof a image processing pipeline or a directed acyclic graph (DAG) and thedevelopment environment may be equipped to actually present thedeveloper with a representation of the program code being developed assuch. Kernels may be developed by a developer individually and/or may beprovided by an entity that supplies any underlying technology (such asthe actual signal processor hardware and/or a design thereof) and/or bya third party (e.g., a vendor of kernel software written for thedevelopment environment). As such, it is expected that a nominaldevelopment environment will include a “library” of kernels thatdevelopers are free to “hook-up” in various ways to effect the overallflow of their larger development effort. Some basic kernels that areexpected to be part of such a library may include kernels to provide anyone or more of the following basic image processing tasks: convolutions,denoising, color space conversions, edge and corner detection,sharpening, white balance, gamma correction, tone mapping, matrixmultiply, image registration, pyramid construction, wavelettransformation, block-wise discrete cosine, and Fourier transformations.

FIG. 2b shows an exemplary depiction of the structure of a kernel 203 asmay be envisioned by a developer. As observed in FIG. 2b , the kernel203 can be viewed as a number of parallel threads of program code(“threads”) 204 that are each operating on a respective underlyingprocessor 205 where each processor 205 is directed to a particularlocation in an output array 206 (such as a specific pixel location inthe output image that the kernel is generating). For simplicity onlythree processors and corresponding threads are shown in FIG. 2b . Invarious embodiments, every depicted output array location would have itsown dedicated processor and corresponding thread. That is, a separateprocessor and thread can be allocated for each pixel in the outputarray. In alternative approaches, a same thread may generate data formore than output pixel and/or two different threads (e.g., in certainlimited cases) may collaborate on the generation of the data for a sameoutput pixel.

As will be described in more detail below, in various embodiments, inthe actual underlying hardware an array of execution lanes andcorresponding threads operate in unison (e.g., in a Single InstructionMultiple Data (SIMD) like fashion) to generate output image data for aportion of a “line group” of the frame currently being processed. A linegroup is a contiguous, sizable section of an image frame. In variousembodiments, the developer may be conscious the hardware operates online groups, or, the development environment may present an abstractionin which there is a separate processor and thread for, e.g., every pixelin the output frame (e.g., every pixel in an output frame generated byits own dedicated processor and thread). Regardless, in variousembodiments, the developer understands the kernel to include anindividual thread for each output pixel (whether the output array isvisualized as an entire output frame or a section thereof).

As will be described in more detail below, in an embodiment theprocessors 205 that are presented to the developer in the virtualenvironment have an instruction set architecture (ISA) that, not onlysupports standard (e.g., RISC) opcodes, but also includes speciallyformatted data access instructions that permit the developer to easilyvisualize the pixel by pixel processing that is being performed. Theability to easily define/visualize any input array location incombination with an entire ISA of traditional mathematical and programcontrol opcodes allows for an extremely versatile programmingenvironment that essentially permits an application program developer todefine, ideally, any desired function to be performed on any sized imagesurface. For example, ideally, any mathematical operation can be readilyprogrammed to be applied to any stencil size.

With respect to the data access instructions, in an embodiment the ISAof the virtual processors (“virtual ISA”) include a special data loadinstruction and a special data store instruction. The data loadinstruction is able to read from any location within an input array ofimage data. The data store instruction is able to write to any locationwithin the output array of image data. The latter instruction allows foreasily dedicating multiple instances of the same processor to differentoutput pixel locations (each processor writes to a different pixel inthe output array). As such, for example, stencil size itself (e.g.,expressed as a width of pixels and a height of pixels) can be made aneasily programmable feature. Visualization of the processing operationsis further simplified with each of the special load and storeinstructions having a special instruction format whereby target arraylocations are specified simplistically as X and Y coordinates.

Regardless, by instantiating a separate processor for each of multiplelocations in the output array, the processors can execute theirrespective threads in parallel so that, e.g., the respective values forall locations in the output array are produced concurrently. It isnoteworthy that many image processing routines typically perform thesame operations on different pixels of the same output image. As such,in one embodiment of the development environment, each processor ispresumed to be identical and executes the same thread program code.Thus, the virtualized environment can be viewed as a type oftwo-dimensional (2D), SIMD processor composed of a 2D array of, e.g.,identical processors each executing identical code in lock-step.

FIG. 3 shows a more detailed example of the processing environment fortwo virtual processors that are processing identical code for twodifferent pixel locations in an output array. FIG. 3 shows an outputarray 304 that corresponds to an output image being generated. Here, afirst virtual processor is processing the code of thread 301 to generatean output value at location X1 of the output array 304 and a secondvirtual processor is processing the code of thread 302 to generate anoutput value at location X2 of the output array 304. Again, in variousembodiments, the developer would understand there is a separateprocessor and thread for each pixel location in the output array 304(for simplicity FIG. 3 only shows two of them). However, the developerin various embodiments need only develop code for one processor andthread (because of the SIMD like nature of the machine).

As is known in the art, an output pixel value is often determined byprocessing the pixels of an input array that include and surround thecorresponding output pixel location. For example, as can be seen fromFIG. 3, position X1 of the output array 304 corresponds to position E ofthe input array 303. The stencil of input array 303 pixel values thatwould be processed to determine output value X1 would thereforecorresponds to input values ABCDEFGHI. Similarly, the stencil of inputarray pixels that would be processed to determine output value X2 wouldcorresponds to input values DEFGHIJKL.

FIG. 3 shows an example of corresponding virtual environment programcode for a pair of threads 301, 302 that could be used to calculateoutput values X1 and X2, respectively. In the example of FIG. 3 bothpairs of code are identical and average a stencil of nine input arrayvalues to determine a corresponding output value. The only differencebetween the two threads is the variables that are called up from theinput array and the location of the output array that is written to.Specifically, the thread that writes to output location X1 operates onstencil ABCDEFGHI and the thread that writes to output location X2operates on stencil DEFGHIJKL.

As can be seen from the respective program code from the pair of threads301, 302, each virtual processor at least includes internal registers R1and R2 and at least supports the following instructions: 1) a LOADinstruction from the input array into R1; 2) a LOAD instruction from theinput array into R2; 3) an ADD instruction that adds the contents of R1and R2 and places the resultant in R2; 4) a DIV instruction that dividesthe value within R2 by immediate operand 9; and, 5) a STORE instructionthe stores the contents of R2 into the output array location that thethread is dedicated to. Again, although only two output array locationsand only two threads and corresponding processors are depicted in FIG.3, conceivably, every location in the output array could be assigned avirtual processor and corresponding thread that performs thesefunctions. In various embodiments, in keeping with the SIMD-like natureof the processing environment, the multiple threads execute in isolationof one another. That is, there is no thread-to-thread communicationbetween virtual processors (one SIMD channel is preventing from crossinginto another SIMD channel).

b. Virtual Processor Memory Model

In various embodiments, a pertinent feature of the virtual processors istheir memory model. As is understood in the art, a processor reads datafrom memory, operates on that data and writes new data back into memory.A memory model is the perspective or view that a processor has of themanner in which data is organized in memory. FIGS. 4a-4c pertain to anembodiment of the memory model for the virtual processors of thedevelopment environment. A simplistic environment involving only threevirtual processors and corresponding threads 401 is used for purposes ofexample. As will be described in more detail below, the memory model ofthe virtual processors takes care to preserve SIMD semantics while, atthe same time, provide for scalar operations and private intermediatevalue storage space for each virtual processor.

As observed in FIG. 4a , in an embodiment, the memory region 420 thateach virtual processor operates out of is organized into six differentpartitions based on the type of information that is stored.Specifically, there exists: 1) a private scratchpad region 402; 2) aglobal input data array region 403; 3) a global output data array region404; 4) a global look-up table information region 405; 5) a globalatomic statistics region 406; and, 6) a global constant tableinformation region 407.

The partitions as depicted in FIG. 4a attempt to visualize those regionsof memory that are shared or “global” amongst virtual processors inkeeping with the SIMD-like nature of the overall processing environment.Likewise, FIG. 4a also attempts to visualize other regions of memorythat are not shared amongst virtual processors or are “private” to aparticular virtual processor. Specifically, as observed in FIG. 4a , allof the memory partitions are global with the exception of a scratchpadregion 402 that is private to each virtual processor. A number of thedifferent memory regions also have different memory addressing schemesas described further below.

With respect to the scratch pad region 402, it is not uncommon totemporarily store intermediate information over the course of executionof a sophisticated image processing algorithm (e.g., and then read theinformation back and use it a later time). Additionally, it is notuncommon for such information to be different across threads (differentinput values may effect different intermediate values). The memory modeltherefore includes per processor private scratchpad regions 402 for thestorage of such intermediate information by each virtual processor'scorresponding thread. In an embodiment, the scratch pad region for aparticular processor is accessed 409 by that processor through a typical(e.g., linear) random access memory address and is a read/write regionof memory (i.e., a virtual processor is able to both read informationfrom private memory as well as write information into private memory).Embodiments of the virtual processor ISA instruction format foraccessing the scratchpad region are discussed in more detail furtherbelow.

The input array portion 403 contains the set of input data that iscalled into 408 the set of threads in order to produce output data. In atypical situation the input array corresponds to an image (e.g., aframe) or section of an image that each thread is operating on orwithin. The input image may be a true input such as the pixelinformation provided by a camera, or, some form of intermediate imagesuch as the information provided by a previous kernel in a largeroverall image processing sequence. Virtual processors typically do notcompete for same input data items because they operate on differentpixel locations of the input image data during a same cycle.

In an embodiment, a novel memory addressing scheme is used to definewhich particular input values are to be called in from the input array403. Specifically, a “position relative” addressing scheme is used thatdefines the desired input data with X, Y coordinates rather than atraditional linear memory address. As such, the load instruction of thevirtual processors' ISA includes an instruction format that identifies aspecific memory location within the input array with an X component anda Y component. As such, a two-dimensional coordinate system is used toaddress memory for input values read from the input array 403.

The use of a position relative memory addressing approach permits theregion of an image that a virtual processor is operating on to be morereadily identifiable to a developer. As mentioned above, the ability toeasily define/visualize any input array location in combination with anentire ISA of traditional mathematical and program control opcodesallows for an extremely versatile programming environment thatessentially permits an application program developer to readily define,ideally, any desired function to be performed on any sized imagesurface. Various instruction format embodiments for instructions thatadopt a position relative addressing scheme, as well as embodiments ofother features of the supported ISA, are described in more detailfurther below.

The output array 404 contains the output image data that the threads areresponsible for generating. The output image data may be final imagedata such as the actual image data that is presented on a display thatfollows the overall image processing sequence, or, may be intermediateimage data that a subsequent kernel of the overall image processingsequence uses as its input image data information. Again, virtualprocessors typically do not compete for same output data items becausethey write to different pixel locations of the output image data duringa same cycle.

In an embodiment, the position relative addressing scheme is also usedfor writes to the output array. As such, the ISA for each virtualprocessor includes a store instruction whose instruction format definesa targeted write location in memory as a two-dimensional X, Y coordinaterather than a traditional random access memory address. More detailsconcerning embodiments of the position relative instructions of thevirtual ISA are provided further below.

FIG. 4a also shows each virtual processor performing a look-up 410 intoa look-up table 411 that is kept within the look-up table memory region405. Look-up tables are often used by image processing tasks to, e.g.,obtain filter or transform coefficients for different array locations,implement complex functions (e.g., gamma curves, sine, cosine) where thelook-up table provides the function output for an input index value,etc. Here, it is expected that SIMD image processing sequences willoften perform a look-up into a same look-up table during a same clockcycle. As such, like the input and output array memory regions 403, 404,the look-up table region 405 is globally accessible by any virtualprocessor. FIG. 4a likewise shows each of the three virtual processorseffectively looking-up information from a same look-up table 411 kept inthe look-up table memory region 405.

In an embodiment, as index values are typically used to define a desiredlook-up table entry, the look-up table information region is accessedusing a normal linear accessing scheme. In an embodiment the look-upregion of memory is read only (i.e., the processor can not changeinformation in a look-up table and is only permitted to read informationfrom it). For simplicity FIG. 4a suggests only one look-up table isresident within the look-up table region 405 but the virtual environmentpermits for multiple, different look-up tables to be resident during thesimulated runtime. Embodiments of the virtual ISA instruction format forinstructions that perform look-ups into the look-up table are providedfurther below.

FIG. 4b shows each of the three virtual processors writing 413 to theatomic statistics region 406. It is not uncommon for image processes to“update” or make a modest change to output information. The updatedinformation may then be used for other downstream processes that makeuse of the updated information. Examples of such updates or modestchanges include simple additions of a fixed offset to output data,simple multiplication of a multiplicand against output data, or minimumor maximum comparisons of output data against some threshold.

In these sequences, as observed in FIG. 4b , output data that has justbeen calculated by the individual threads 401 may be operated upon andthe resultants written 413 to the atomic statistics region 406.Depending on implementation semantics, the output data that is operatedon by an atomic act may be kept internally by the processor or called up412 from the output array, FIG. 4b shows the later. In variousembodiments, the atomic acts that may be performed on the output datainclude add, multiply, min, and max. In an embodiment, the atomicstatistics region 406 is accessed using a position relative addressingscheme (as with input and output array accesses) given that updates tooutput data would logically be organized in a same two dimensional arrayas the output data itself. Embodiments of the virtual ISA instructionformat for performing an atomic act on output data and writing theresultant to the statistics region 406 are described in more detailfurther below.

FIG. 4c shows each of the virtual processors reading 414 a constantvalue from a constant look-up table 415 within the constant memoryregion 407. Here, e.g., it is expected that different threads 401 mayneed a same constant or other value on the same clock cycle (e.g., aparticular multiplier to be applied against an entire image). Thus,accesses into the constant look-up table 415 return a same, scalar valueto each of the virtual processors as depicted in FIG. 4c . Becauselook-up tables are typically accessed with an index value, in anembodiment, the constant look-up table memory region is accessed with alinear random access memory address. In an embodiment the constantregion of memory is read only (i.e., the processor can not changeinformation in a constant table and is only permitted to readinformation from it). For simplicity FIG. 4c only shows a singleconstant look-up table 415 in the constant memory region 407. As threadsmay make use of more than one such table memory region 407 is configuredto be large enough to hold as many constant tables are needed/used.

c. Virtual Processor ISA

As alluded to above in multiple instances, the virtual processor ISA mayinclude a number of pertinent features. Some of these described atlength immediately below.

In various embodiment the instruction format of each virtual processor'sISA uses a relative positioning approach to define an X, Y coordinatefor each of the following: 1) a LOAD instruction that reads input imagedata from the input array memory region; 2) a STORE instruction thatwrites output image data to the output array; and, 3) an atomic updateto the statistics region of memory.

The ability to easily define any input array location in combinationwith an entire ISA of traditional data access, mathematical, and programcontrol opcodes allows for an extremely versatile programmingenvironment that essentially permits an application program developer todefine, ideally, any desired function to be performed on any sized imagesurface. For example, ideally, any mathematical operation can be readilyprogrammed to be applied to any stencil size.

In an embodiment, instructions for loads/stores from/to the input/outputarrays have the following format

-   -   [OPCODE] LINEGROUP_(name)[(((X*XS+X0)/XD);((Y*YS+Y0)/YD); Z]        where [OPCODE] is the specific type of operation (LOAD from the        input array, STORE to the output array) and LINEGROUP_(name) is        the name assigned to a particular section of a particular image        (e.g., a line group for a frame of image data) within the input        or output array memory region. Here, because different line        groups are operated on separately, the different linegroups are        given different names so they can be uniquely        identified/accessed (e.g., LINEGROUP_1, LINEGROUP_2, etc.). Line        groups of same name may exist in both the input array memory        region and the output array memory region. The origin of any        line group may be, e.g., its lower left hand corner within its        appropriate memory region.

In the case of instructions that perform updates on the atomicstatistics table, in an embodiment, the instruction format takes on thefollowing similar structure

-   -   [OPCODE] STATS_(name)[(((X*XS+X0)/XD);((Y*YS+Y0)/YD); Z]        with the notable difference being that the input operand        information defines a position within a particular statistics        table (STATS_(name)) rather than a particular line group within        the input or output array. As with line groups, different names        are given to different statistics tables so that a thread can        uniquely operate on different statistics tables over the course        of its operation. The [OPCODE] specifies the particular atomic        act to be performed (e.g., STAT_ADD; STAT_MUL; STAT_MIN;        STAT_MAX).

For either input/output array accesses or atomic statistics tableaccesses, the Z operand of the instruction defines which channel of anamed line group or stats table is targeted by the instruction. Here,typically, a single image will have multiple channels. For example,video images typically have a red channel (R), a green channel (G), anda blue channel (B) for a same frame of the video stream. In a sense, acomplete image can be viewed as separate R, G, and B channel imagesstacked on top of each other. The Z operand defines which one of theseis targeted by the instruction (e.g., Z=0 corresponds to the redchannel, Z=1 corresponds to the blue channel, and Z=2 corresponds to thegreen channel). Each line group and statistics table is thereforestructured to include the content of each channel for the particularimage being processed.

The (X*XS+X0)/XD operand defines the X location within a named linegroup or stats table that is targeted by the instruction and the(Y*YS+Y0)/YD operand defines the Y location within a named line group orstats table that is targeted by the instruction. The XS and XD terms forthe X location and the YS and YD terms for the Y location are used forscaling between input and output images having different pixeldensities. Scaling is described in more detail further below.

In a simplest case, there is no scaling between input and output imagesand the X and Y components of the instruction format simply take theform of X+X0 and Y+Y0 where X0 and Y0 are positional offsets relative tothe position of the thread. A thread is viewed as being assigned to theposition within the output array line group that its output value iswritten to. A corresponding, same position is readily identifiable inthe input array line group and any stats table.

As an example, if the thread is assigned a specific X, Y location in anoutput array LINEGROUP_1, the instruction

-   -   LOAD LINEGROUP_1[(X−1);(Y−1);Z]        would load from LINEGROUP_1 a value that is to the left one        pixel location and down one pixel location from the same X,Y        position within the input array.

A simple blur kernel that averages together the pixel values for the X,Ylocation along with its left and right neighbors may therefore bewritten in pseudo-code as depicted in FIG. 5a . As observed in FIG. 5a ,the location ((X);(Y)) corresponds to the position of the virtualprocessor that is writing to the output array. In the above pseudo-code,LOAD corresponds to the opcode for a load from the input array and STOREcorresponds to the opcode for the store to the output array. Note thatthere exists a LINEGROUP_1 in the input array and a LINEGROUP_1 in theoutput array.

FIG. 5b depicts scaled images for purposes of explaining the scalingfeatures of the relative positioning load and store instruction format.Down sampling refers to the transformation of a higher resolution imageto a lower resolution image by providing in the output image less thanall of the pixels that exist in the input image. Up sampling refers tothe transformation of a lower resolution image to a higher resolutionimage by creating more pixels in the output image than exist in theinput image.

For example, referring to FIG. 5b , if image 501 represents the inputimage and image 502 represents the output image, down sampling will beperformed because there are less pixels in the output image than in theinput image. Here, for each pixel in the output image, the pertinentpixels in the input image that determine the output value for an outputpixel progress “farther away” from the output pixel location movingalong either axis in the output image. For example, for a 3:1 downsampling ratio, the first pixel in the output image along either axiscorresponds to the first, second, and third pixels along the same axisin the input image, the second pixel in the output image corresponds tothe fourth, fifth, and sixth pixels in the input image, etc. Thus thefirst output pixel has a pertinent pixel in the third location while thesecond output pixel has a pertinent pixel in the sixth location.

As such, the XS and YS multiplicand terms in the relative positioninginstruction format are used to implement down sampling. If the blurpseudo code of FIG. 5a where to be rewritten for 3:1 down sampling alongboth axis, the code would be rewritten as:

R1<=LOAD LINEGROUP_1[((3X)−1);3(Y);0] R2<=LOAD LINEGROUP_1[3(X);3(Y);0]R3<=LOAD LINEGROUP_1[((3X)+1);3(Y);0] R2<=ADD R1, R2 R2<=ADD R2, R3R2<=DIV R2, 3 STORE LINEGROUP_1[(X);(Y);(0)]; R2.

By contrast, in the case of 1:3 up sampling (e.g., image 502 is theinput image and image 501 is the output image) the XD and YD divisorswould be used to create three output pixels for every input pixel alongeither axis. As such, the blur code would be rewritten as:

R1<=LOAD LINEGROUP_1[(X−1)/3;(Y)/3;0] R2<=LOADLINEGROUP_1[(X)/3;(Y)/3;0] R3<=LOAD LINEGROUP_1[(X+1)/3;(Y)/3;0] R2<=ADDR1, R2 R2<=ADD R2, R3 R2<=DIV R2, 3 STORE LINEGROUP_1[(X);(Y);(0)]; R2

In various embodiments the instruction format for instructions thataccess the private, constant, and look-up portions of memory include anoperand that also take the form of a*b+c where a is a base position, bis a scaling term and c is an offset. Here, however, a linear addressingapproach is taken where the a*b+c term essentially corresponds to alinear index that is applied to the targeted table. Each of theseinstructions also include in the opcode and an identifier of the memoryregion being accessed. For example, an instruction that performs alook-up from the look-up table memory region may be expressed as

-   -   LOAD LKUP_(name)[(A*B+C)].        where LOAD is the opcode that identifies a load operation and        LKUP_(name) specifies the name of the look-up table in the        look-up table memory region being accessed. Again, multiple        look-up tables may be used by a thread and therefore a naming        scheme is used to identify the appropriate one of the more than        one that exist in the look-up table memory region.

A similar format with similarly minded opcode may be utilized forinstructions that target the constant and the private memory regions(e.g., LOAD CNST_(name)[(A*B+C)]; LOAD PRVT_(name)[(A*B+C)]. In anembodiment, look-up table and the constant table accesses are read-only(a processor can not change the data that has been placed there). Assuch no STORE instructions exist for these memory regions. In anembodiment the private region of memory is read/write. As such a storeinstruction exists for that memory region (e.g., STORE PRVT[(A*B+C)].

In various embodiments, each virtual processor includes general purposeregisters that can contain integer, floating point or fixed pointvalues. Additionally, the general purpose registers may contain datavalues of configurable bit width such as 8, 16 or 32 bit values. Thus,the image data at each pixel location in an input array or output arraycan have a data size of 8, 16 or 32 bits. Here, a virtual processor canbe configured for an execution mode that establishes the bit size andthe numerical format of the values within the general purpose registers.Instructions may also specify immediate operands (which are inputoperands whose input values are expressed directly in the instructionitself rather being found in a specified register). Immediate operandscan also have configurable 8, 16 or 32 bit widths.

In an extended embodiment, each virtual processor is also capable ofoperating in a scalar mode or a SIMD mode internal to itself. That is,the data within a specific array location may be viewed as a scalarvalue or as a vector having multiple elements. For example a firstconfiguration may establish scalar operation of 8 bits where each imagearray position holds a scalar 8 bit value. By contrast anotherconfiguration may establish parallel/SIMD operation of 32 bits whereeach image array location is assumed to hold four 8 bit values for atotal data size of 32 bits per array location.

In various embodiments each virtual processor also includes registers tohold predicate values. A single predicate value is often only one bit inlength and expresses a resultant from an opcode that performs atrue/false or greater than/less than test on existing data. Predicatevalues are used, e.g., to determine branch directions through the codeduring execution (and therefore are used as operands in conditionalbranch instructions). Predicate values can also be expressed as animmediate operand in an instruction.

In various embodiments each virtual processor includes registers to holdscalar values. Here, scalar values are stored into and read from thepartition space of the memory model that is reserved for constants (asdiscussed above with respect to FIG. 4c ). Here, each virtual processorof a group of virtual processors that are processing a same image usesthe same scalar value from the constant memory space. In extendedembodiments scalar predicates also exist. These are values kept inregister space that meet the definition of both a predicate and ascalar.

In various embodiments each virtual processor is designed as a RISC-likeinstruction set whose supported arithmetic instruction opcodes includeany workable combination of the following: 1) ADD (addition of operandsA and B); 2) SUB (subtraction of operands A and B); 3) MOV (move operandfrom one register to another register); 4) MUL (multiple operands A andB); 5) MAD (multiply operands A and B and add C to resultant); 6) ABS(return absolute value of operand A); 7) DIV (divide operand A byoperand B); 8) SHL (shift operand A to the left); 9) SHR (shift operandA to the right); 10) MIN/MAX (return which of operands A and B isgreater); 11) SEL (select specified bytes of operand A); 12) AND (returnthe logical AND of operands A and B); 13) OR (return the logical OR ofoperands A and B); 14) XOR (return the logical exclusive OR of operandsA and B); 15) NOT (return the logical inverse of operand A).

The instruction set also includes standard predicate operations suchas: 1) SEQ (returns a 1 if A equals B); 2) SNE (returns a 1 if A doesnot equal B); 3) SLT (returns a 1 if A is less than B); 4) SLE (returnsa 1 if A is less than or equal to B). Control flow instructions are alsoincluded such as JMP (jump) and BRANCH each of which may include nominalvariables or predicates as operands.

d. Application Software Development and Simulation Environment

FIG. 6 depicts an application software development and simulationenvironment 601. As discussed above with respect to FIG. 2, a developermay develop a comprehensive image processing function (e.g., an imageprocessing pipeline where each stage in the pipeline performs adedicated image processing task, some other DAG prescribed set ofroutines, etc.) by arranging kernels in a strategic sequence that isconsistent with the overall intended image transformation. Kernels maybe called up from a library 602 and/or the developer may develop one ormore custom kernels.

Kernels within the library 602 may be provided by a third party vendorof kernels and/or a provider of any underlying technology (e.g., avendor of a hardware platform that includes the targeted hardware imageprocessor or a vendor of the targeted hardware image processor (e.g.,provided as a design thereof or as actual hardware)).

In the case of custom developed kernels, in many situations thedeveloper need only write the program code for a single thread 603. Thatis, the developer need only write program code that determines a singleoutput pixel value by referencing input pixel values relative to theoutput pixel location (e.g., with the aforementioned position relativememory access instruction format). Upon satisfaction of the operation ofthe single thread 603, the development environment may thenautomatically instantiate multiple instances of the thread code on arespective virtual processor to effect a kernel on an array ofprocessors that operate on an image surface area. The image surface areamay be a section of an image frame (such as a line group).

In various embodiments, the custom thread program code is written in theobject code of the virtual processor ISA (or a higher level languagethat is compiled down to the virtual processor ISA object code).Simulation of execution of the custom kernel's program code may beperformed in a simulated runtime environment that includes a virtualprocessor accessing a memory organized according to the memory model.Here, software models (object oriented or otherwise) of a virtualprocessor 604 and a memory 605 that incorporates the model areinstantiated.

The virtual processor model 604 then simulates execution of the threadcode 603. Upon satisfaction of the performance of a thread, its largerkernel and any larger function that the kernel belongs to, the whole iscompiled into the actual object code of the underlying hardware. Theentirety of the simulation environment 601 may be implemented assoftware that runs on a computer system (e.g., a workstation) 606.

2.0 Hardware Architecture Embodiments

a. Image Processor Hardware Architecture and Operation

FIG. 7 shows an embodiment of an architecture 700 for an image processorimplemented in hardware. The image processor may be targeted, forexample, by a compiler that converts program code written for a virtualprocessor within a simulated environment into program code that isactually executed by the hardware processor. As observed in FIG. 7, thearchitecture 700 includes a plurality of line buffer units 701_1 through701_M (hereinafter “line buffers”, “line buffer units” or the like)interconnected to a plurality of stencil processor units 702_1 through702_N (hereinafter, “stencil processors”, “stencil processor units” orthe like) and corresponding sheet generator units 703_1 through 703_N(hereinafter “sheet generators”, “sheet generator units” or the like)through a network 704 (e.g., a network on chip (NOC) including an onchip switch network, an on chip ring network or other kind of network).In an embodiment, any line buffer unit may connect to any sheetgenerator and corresponding stencil processor through the network 704.

In an embodiment, program code is compiled and loaded onto acorresponding stencil processor 702 to perform the image processingoperations earlier defined by a software developer (program code mayalso be loaded onto the stencil processor's associated sheet generator703, e.g., depending on design and implementation). In at least someinstances an image processing pipeline may be realized by loading afirst kernel program for a first pipeline stage into a first stencilprocessor 702_1, loading a second kernel program for a second pipelinestage into a second stencil processor 702_2, etc. where the first kernelperforms the functions of the first stage of the pipeline, the secondkernel performs the functions of the second stage of the pipeline, etc.and additional control flow methods are installed to pass output imagedata from one stage of the pipeline to the next stage of the pipeline.

In other configurations, the image processor may be realized as aparallel machine having two or more stencil processors 702_1, 702_2operating the same kernel program code. For example, a highly dense andhigh data rate stream of image data may be processed by spreading framesacross multiple stencil processors each of which perform the samefunction.

In yet other configurations, essentially any DAG of kernels may beloaded onto the hardware processor by configuring respective stencilprocessors with their own respective kernel of program code andconfiguring appropriate control flow hooks into the hardware to directoutput images from one kernel to the input of a next kernel in the DAGdesign.

As a general flow, frames of image data are received by a macro I/O unit705 and passed to one or more of the line buffer units 701 on aframe-by-frame basis. A particular line buffer unit parses its frame ofimage data into a smaller region of image data, referred to as a “linegroup”, and then passes the line group through the network 704 to aparticular sheet generator. A complete or “full” singular line group maybe composed, for example, with the data of multiple contiguous completerows or columns of a frame (for brevity the present specification willmainly refer to contiguous rows). The sheet generator further parses theline group of image data into a smaller region of image data, referredto as a “sheet”, and presents the sheet to its corresponding stencilprocessor.

In the case of an image processing pipeline or a DAG flow having asingle input, generally, input frames are directed to the same linebuffer unit 701_1 which parses the image data into line groups anddirects the line groups to the sheet generator 703_1 whose correspondingstencil processor 702_1 is executing the code of the first kernel in thepipeline/DAG. Upon completion of operations by the stencil processor702_1 on the line groups it processes, the sheet generator 703_1 sendsoutput line groups to a “downstream” line buffer unit 701_2 (in some usecases the output line group may be sent_back to the same line bufferunit 701_1 that earlier had sent the input line groups).

One or more “consumer” kernels that represent the next stage/operationin the pipeline/DAG executing on their own respective other sheetgenerator and stencil processor (e.g., sheet generator 703_2 and stencilprocessor 702_2) then receive from the downstream line buffer unit 701_2the image data generated by the first stencil processor 702_1. In thismanner, a “producer” kernel operating on a first stencil processor hasits output data forwarded to a “consumer” kernel operating on a secondstencil processor where the consumer kernel performs the next set oftasks after the producer kernel consistent with the design of theoverall pipeline or DAG.

A stencil processor 702 is designed to simultaneously operate onmultiple overlapping stencils of image data. The multiple overlappingstencils and internal hardware processing capacity of the stencilprocessor effectively determines the size of a sheet. Here, within astencil processor 702, arrays of execution lanes operate in unison tosimultaneously process the image data surface area covered by themultiple overlapping stencils.

As will be described in more detail below, in various embodiments,sheets of image data are loaded into a two-dimensional register arraystructure within the stencil processor 702. The use of sheets and thetwo-dimensional register array structure is believed to effectivelyprovide for power consumption improvements by moving a large amount ofdata into a large amount of register space as, e.g., a single loadoperation with processing tasks performed directly on the dataimmediately thereafter by an execution lane array. Additionally, the useof an execution lane array and corresponding register array provide fordifferent stencil sizes that are easily programmable/configurable.

FIGS. 8a through 8e illustrate at a high level embodiments of both theparsing activity of a line buffer unit 701, the finer grained parsingactivity of a sheet generator unit 703, as well as the stencilprocessing activity of the stencil processor 702 that is coupled to thesheet generator unit 703.

FIG. 8a depicts an embodiment of an input frame of image data 801. FIG.8a also depicts an outline of three overlapping stencils 802 (eachstencil having a dimension of 3 pixels by 3 pixels) that a stencilprocessor is designed to operate over. The output pixel that eachstencil respectively generates output image data for is highlighted insolid black. For brevity, the three overlapping stencils 802 aredepicted as overlapping only in the vertical direction. It is pertinentto recognize that in actuality a stencil processor may be designed tohave overlapping stencils in both the vertical and horizontaldirections.

Because of the vertical overlapping stencils 802 within the stencilprocessor, as observed in FIG. 8a , there exists a wide band of imagedata within the frame that a single stencil processor can operate over.As will be discussed in more detail below, in an embodiment, the stencilprocessors process data within their overlapping stencils in a left toright fashion across the image data (and then repeat for the next set oflines, in top to bottom order). Thus, as the stencil processors continueforward with their operation, the number of solid black output pixelblocks will grow right-wise horizontally. As discussed above, a linebuffer unit 701 is responsible for parsing a line group of input imagedata from an incoming frame that is sufficient for the stencilprocessors to operate over for an extended number of upcoming cycles. Anexemplary depiction of a line group is illustrated as a shaded region803. In an embodiment, as described further below, the line buffer unit701 can comprehend different dynamics for sending/receiving a line groupto/from a sheet generator. For example, according to one mode, referredto as “full group”, the complete full width lines of image data arepassed between a line buffer unit and a sheet generator. According to asecond mode, referred to as “virtually tall”, a line group is passedinitially with a subset of full width rows. The remaining rows are thenpassed sequentially in smaller (less than full width) pieces.

With the line group 803 of the input image data having been defined bythe line buffer unit and passed to the sheet generator unit, the sheetgenerator unit further parses the line group into finer sheets that aremore precisely fitted to the hardware limitations of the stencilprocessor. More specifically, as will be described in more detailfurther below, in an embodiment, each stencil processor consists of atwo dimensional shift register array. The two dimensional shift registerarray essentially shifts image data “beneath” an array of executionlanes where the pattern of the shifting causes each execution lane tooperate on data within its own respective stencil (that is, eachexecution lane processes on its own stencil of information to generatean output for that stencil). In an embodiment, sheets are surface areasof input image data that “fill” or are otherwise loaded into the twodimensional shift register array.

Thus, as observed in FIG. 8b , the sheet generator parses an initialsheet 804 from the line group 803 and provides it to the stencilprocessor (here, the exemplary sheet of data corresponds to the five byfive shaded region that is generally identified by reference number804). As observed in FIGS. 8c and 8d , the stencil processor operates onthe sheet of input image data by effectively moving the overlappingstencils 802 in a left to right fashion over the sheet. As of FIG. 8d ,the number of pixels for which an output value could be calculated (ninein a darkened 3 by 3 array) from the data within the sheet is exhausted(no other pixel positions can have an output value determined from theinformation within the sheet). For simplicity the border regions of theimage have been ignored.

As observed in FIG. 8e the sheet generator then provides a next sheet805 for the stencil processor to continue operations on. Note that theinitial positions of the stencils as they begin operation on the nextsheet is the next progression to the right from the point of exhaustionon the first sheet (as depicted previously in FIG. 8d ). With the newsheet 805, the stencils will simply continue moving to the right as thestencil processor operates on the new sheet in the same manner as withthe processing of the first sheet.

Note that there is some overlap between the data of the first sheet 804and the data of the second sheet 805 owing to the border regions ofstencils that surround an output pixel location. The overlap could behandled simply by the sheet generator re-transmitting the overlappingdata twice. In alternate implementations, to feed a next sheet to thestencil processor, the sheet generator may proceed to only send new datato the stencil processor and the stencil processor reuses theoverlapping data from the previous sheet.

b. Stencil Processor Design and Operation

FIG. 9a shows an embodiment of a stencil processor unit architecture900. As observed in FIG. 9a , the stencil processor includes a datacomputation unit 901, a scalar processor 902 and associated memory 903and an I/O unit 904. The data computation unit 901 includes an array ofexecution lanes 905, a two-dimensional shift array structure 906 andseparate respective random access memories 907 associated with specificrows or columns of the array.

The I/O unit 904 is responsible for loading “input” sheets of datareceived from the sheet generator into the data computation unit 901 andstoring “output” sheets of data from the stencil processor into thesheet generator. In an embodiment the loading of sheet data into thedata computation unit 901 entails parsing a received sheet intorows/columns of image data and loading the rows/columns of image datainto the two dimensional shift register structure 906 or respectiverandom access memories 907 of the rows/columns of the execution lanearray (described in more detail below). If the sheet is initially loadedinto memories 907, the individual execution lanes within the executionlane array 905 may then load sheet data into the two-dimensional shiftregister structure 906 from the random access memories 907 whenappropriate (e.g., as a load instruction just prior to operation on thesheet's data). Upon completion of the loading of a sheet of data intothe register structure 906 (whether directly from a sheet generator orfrom memories 907), the execution lanes of the execution lane array 905operate on the data and eventually “write back” finished data as a sheetdirectly back to the sheet generator, or, into the random accessmemories 907. If the execution lanes write back to random accessmemories 907, the I/O unit 904 fetches the data from the random accessmemories 907 to form an output sheet which is then forwarded to thesheet generator.

The scalar processor 902 includes a program controller 909 that readsthe instructions of the stencil processor's program code from scalarmemory 903 and issues the instructions to the execution lanes in theexecution lane array 905. In an embodiment, a single same instruction isbroadcast to all execution lanes within the array 905 to effect singleinstruction multiple data (SIMD)-like behavior from the data computationunit 901. In an embodiment, the instruction format of the instructionsread from scalar memory 903 and issued to the execution lanes of theexecution lane array 905 includes a very-long-instruction-word (VLIW)type format that includes more than one opcode per instruction. In afurther embodiment, the VLIW format includes both an ALU opcode thatdirects a mathematical function performed by each execution lane's ALU(which, as described below, in an embodiment may specify more than onetraditional ALU operation) and a memory opcode (that directs a memoryoperation for a specific execution lane or set of execution lanes).

The term “execution lane” refers to a set of one or more execution unitscapable of executing an instruction (e.g., logic circuitry that canexecute an instruction). An execution lane can, in various embodiments,include more processor-like functionality beyond just execution units,however. For example, besides one or more execution units, an executionlane may also include logic circuitry that decodes a receivedinstruction, or, in the case of more multiple instruction multiple data(MIMD)-like designs, logic circuitry that fetches and decodes aninstruction. With respect to MIMD-like approaches, although acentralized program control approach has largely been described herein,a more distributed approach may be implemented in various alternativeembodiments (e.g., including program code and a program controllerwithin each execution lane of the array 905).

The combination of an execution lane array 905, program controller 909and two dimensional shift register structure 906 provides a widelyadaptable/configurable hardware platform for a broad range ofprogrammable functions. For example, application software developers areable to program kernels having a wide range of different functionalcapability as well as dimension (e.g., stencil size) given that theindividual execution lanes are able to perform a wide variety offunctions and are able to readily access input image data proximate toany output array location.

Apart from acting as a data store for image data being operated on bythe execution lane array 905, the random access memories 907 may alsokeep one or more look-up tables such as any look-up tables held in thelook-up table component of the virtual processing memory described abovein Section 1.0. In various embodiments one or more scalar look-up tablesmay also be instantiated within the scalar memory 903. The one or morescalar look-up tables may be any scalar look-up tables held in thescalar look-up table component of the memory model described above inSection 1.0.

A scalar look-up involves passing the same data value from the samelook-up table from the same index to each of the execution lanes withinthe execution lane array 905. In various embodiments, the VLIWinstruction format described above is expanded to also include a scalaropcode that directs a look-up operation performed by the scalarprocessor into a scalar look-up table. The index that is specified foruse with the opcode may be an immediate operand or fetched from someother data storage location. Regardless, in an embodiment, a look upfrom a scalar look-up table within scalar memory essentially involvesbroadcasting the same data value to all execution lanes within theexecution lane array 905 during the same clock cycle. Additional detailsconcerning the use and operation of look-up tables is provided furtherbelow.

FIG. 9b summarizes the VLIW instruction word embodiments(s) discussedabove. As observed in FIG. 9b , the VLIW instruction word formatincludes fields for three separate instructions: 1) a scalar instruction951 that is executed by the scalar processor; 2) an ALU instruction 952that is broadcasted and executed in SIMD fashion by the respective ALUswithin the execution lane array; and, 3) a memory instruction 953 thatis broadcasted and executed in a partial SIMD fashion (e.g., ifexecution lanes along a same row in the execution lane array share asame random access memory, then one execution lane from each of thedifferent rows actually execute the instruction (the format of thememory instruction 953 may include an operand that identifies whichexecution lane from each row executes the instruction)).

A field 954 for one or more immediate operands is also included. Whichof the instructions 951, 952, 953 use which immediate operandinformation may be identified in the instruction format. Each ofinstructions 951, 952, 953 also includes its own respective inputoperand and resultant information (e.g., local registers for ALUoperations and a local register and a memory address for memory accessinstructions). In an embodiment, the scalar instruction 951 is executedby the scalar processor before the execution lanes within the executionlane array execute either of the other two instructions 952, 953. Thatis, the execution of the VLIW word includes a first cycle upon which thescalar instruction 951 is executed followed by a second cycle upon withthe other instructions 952, 953 may be executed (note that in variousembodiments instructions 952 and 953 may be executed in parallel).

In an embodiment, the scalar instructions executed by the scalarprocessor 902 include commands issued to the sheet generator 703 toload/store sheets from/into the memories or 2D shift register 906 of thedata computation unit 901. Here, the sheet generator's operation can bedependent on the operation of the line buffer unit 701 or othervariables that prevent pre-runtime comprehension of the number of cyclesit will take the sheet generator 703 to complete any command issued bythe scalar processor 902. As such, in an embodiment, any VLIW word whosescalar instruction 951 corresponds to or otherwise causes a command tobe issued to the sheet generator 703 also includes no-operation (NOOP)instructions in the other two instruction fields 952, 953. The programcode then enters a loop of NOOP instructions for instruction fields 952,953 until the sheet generator completes its load/store to/from the datacomputation unit. Here, upon issuing a command to the sheet generator,the scalar processor may set a bit of an interlock register that thesheet generator resets upon completion of the command. During the NOOPloop the scalar processor monitors the bit of the interlock bit. Whenthe scalar processor detects that the sheet generator has completed itscommand normal execution begins again.

FIG. 10 shows an embodiment of a data computation unit 1001. As observedin FIG. 10, the data computation unit 1001 includes an array ofexecution lanes 1005 that are logically positioned “above” atwo-dimensional shift register array structure 1006. As discussed above,in various embodiments, a sheet of image data provided by a sheetgenerator is loaded into the two-dimensional shift register 1006. Theexecution lanes then operate on the sheet data from the registerstructure 1006.

The execution lane array 1005 and shift register structure 1006 arefixed in position relative to one another. However, the data within theshift register array 1006 shifts in a strategic and coordinated fashionto cause each execution lane in the execution lane array to process adifferent stencil within the data. As such, each execution lanedetermines the output image value for a different pixel in the outputsheet being generated. From the architecture of FIG. 10 it should beclear that overlapping stencils are not only arranged vertically butalso horizontally as the execution lane array 1005 includes verticallyadjacent execution lanes as well as horizontally adjacent executionlanes.

Some notable architectural features of the data computation unit 1001include the shift register structure 1006 having wider dimensions thanthe execution lane array 1005. That is, there is a “halo” of registers1009 outside the execution lane array 1005. Although the halo 1009 isshown to exist on two sides of the execution lane array, depending onimplementation, the halo may exist on less (one) or more (three or four)sides of the execution lane array 1005. The halo 1005 serves to provide“spill-over” space for data that spills outside the bounds of theexecution lane array 1005 as the data is shifting “beneath” theexecution lanes 1005. As a simple case, a 5×5 stencil centered on theright edge of the execution lane array 1005 will need four halo registerlocations further to the right when the stencil's leftmost pixels areprocessed. For ease of drawing, FIG. 10 shows the registers of the rightside of the halo as only having horizontal shift connections andregisters of the bottom side of the halo as only having vertical shiftconnections when, in a nominal embodiment, registers on either side(right, bottom) would have both horizontal and vertical connections.

Additional spill-over room is provided by random access memories 1007that are coupled to each row and/or each column in the array, orportions thereof (e.g., a random access memory may be assigned to a“region” of the execution lane array that spans 4 execution lanes rowwise and 2 execution lanes column wise. For simplicity the remainder ofthe application will refer mainly to row and/or column based allocationschemes). Here, if an execution lane's kernel operations require it toprocess pixel values outside of the two-dimensional shift register array1006 (which some image processing routines may require) the plane ofimage data is able to further spill-over, e.g., from the halo region1009 into random access memory 1007. For example, consider a 6×6 stencilwhere the hardware includes a halo region of only four storage elementsto the right of an execution lane on the right edge of the executionlane array. In this case, the data would need to be shifted further tothe right off the right edge of the halo 1009 to fully process thestencil. Data that is shifted outside the halo region 1009 would thenspill over to random access memory 1007. Other applications of therandom access memories 1007 and the stencil processor of FIG. 3 areprovided further below.

FIGS. 11a through 11k demonstrate a working example of the manner inwhich image data is shifted within the two-dimensional shift registerarray “beneath” the execution lane array as alluded to above. Asobserved in FIG. 11a , the data contents of the two-dimensional shiftarray are depicted in a first array 1107 and the execution lane array isdepicted by a frame 1105. Also, two neighboring execution lanes 1110within the execution lane array are simplistically depicted. In thissimplistic depiction 1110, each execution lane includes a register R1that can accept data from the shift register, accept data from an ALUoutput (e.g., to behave as an accumulator across cycles), or writeoutput data into an output destination.

Each execution lane also has available, in a local register R2, thecontents “beneath” it in the two-dimensional shift array. Thus, R1 is aphysical register of the execution lane while R2 is a physical registerof the two-dimensional shift register array. The execution lane includesan ALU that can operate on operands provided by R1 and/or R2. As will bedescribed in more detail further below, in an embodiment the shiftregister is actually implemented with multiple (a “depth” of)storage/register elements per array location but the shifting activityis limited to one plane of storage elements (e.g., only one plane ofstorage elements can shift per cycle). FIGS. 11a through 11k depict oneof these deeper register locations as being used to store the resultantX from the respective execution lanes. For illustrative ease the deeperresultant register is drawn alongside rather than beneath itscounterpart register R2.

FIGS. 11a through 11k focus on the calculation of two stencils whosecentral position is aligned with the pair of execution lane positions1111 depicted within the execution lane array 1105. For ease ofillustration, the pair of execution lanes 1110 are drawn as horizontalneighbors when in fact, according to the following example, they arevertical neighbors.

As observed initially in FIG. 11a , the execution lanes 1111 arecentered on their central stencil locations. FIG. 11b shows the objectcode executed by both execution lanes 1111. As observed in FIG. 11b theprogram code of both execution lanes 1111 causes the data within theshift register array 1107 to shift down one position and shift right oneposition. This aligns both execution lanes 1111 to the upper left handcorner of their respective stencils. The program code then causes thedata that is located (in R2) in their respective locations to be loadedinto R1.

As observed in FIG. 11c the program code next causes the pair ofexecution lanes 1111 to shift the data within the shift register array1107 one unit to the left which causes the value to the right of eachexecution lane's respective position to be shifted into each executionlane′ position. The value in R1 (previous value) is then added with thenew value that has shifted into the execution lane's position (in R2).The resultant is written into R1. As observed in FIG. 11d the sameprocess as described above for FIG. 11c is repeated which causes theresultant R1 to now include the value A+B+C in the upper execution laneand F+G+H in the lower execution lane. At this point both executionlanes 1111 have processed the upper row of their respective stencils.Note the spill-over into a halo region on the left side of the executionlane array 1105 (if one exists on the left hand side) or into randomaccess memory if a halo region does not exist on the left hand side ofthe execution lane array 1105.

As observed in FIG. 11e , the program code next causes the data withinthe shift register array to shift one unit up which causes bothexecution lanes 1111 to be aligned with the right edge of the middle rowof their respective stencils. Register R1 of both execution lanes 1111currently includes the summation of the stencil's top row and the middlerow's rightmost value. FIGS. 11f and 11g demonstrate continued progressmoving leftwise across the middle row of both execution lane's stencils.The accumulative addition continues such that at the end of processingof FIG. 11g both execution lanes 1111 include the summation of thevalues of the top row and the middle row of their respective stencils.

FIG. 11h shows another shift to align each execution lane with itscorresponding stencil's lowest row. FIGS. 11i and 11j show continuedshifting to complete processing over the course of both execution lanes'stencils. FIG. 11k shows additional shifting to align each executionlane with its correct position in the data array and write the resultantthereto.

In the example of FIGS. 11a-11k note that the object code for the shiftoperations may include an instruction format that identifies thedirection and magnitude of the shift expressed in (X, Y) coordinates.For example, the object code for a shift up by one location may beexpressed in object code as SHIFT 0, +1. As another example, a shift tothe right by one location may be expressed in object code as SHIFT +1,0. In various embodiments shifts of larger magnitude may also bespecified in object code (e.g., SHIFT 0, +2). Here, if the 2D shiftregister hardware only supports shifts by one location per cycle, theinstruction may be interpreted by the machine to require multiple cycleexecution, or, the 2D shift register hardware may be designed to supportshifts by more than one location per cycle. Embodiments of the later aredescribed in more detail further below.

FIG. 12 shows another, more detailed depiction of the unit cell for thearray execution lane and shift register structure (registers in the haloregion do not include a corresponding execution lane). The executionlane and the register space that is associated with each location in theexecution lane array is, in an embodiment, implemented by instantiatingthe circuitry observed in FIG. 12 at each node of the execution lanearray. As observed in FIG. 12, the unit cell includes an execution lane1201 coupled to a register file 1202 consisting of four registers R2through R5. During any cycle, the execution lane 1201 may read from orwrite to any of registers R1 through R5. For instructions requiring twoinput operands the execution lane may retrieve both of operands from anyof R1 through R5.

In an embodiment, the two dimensional shift register structure isimplemented by permitting, during a single cycle, the contents of any of(only) one of registers R2 through R4 to be shifted “out” to one of itsneighbor's register files through output multiplexer 1203, and, havingthe contents of any of (only) one of registers R2 through R4 replacedwith content that is shifted “in” from a corresponding one if itsneighbors through input multiplexers 1204 such that shifts betweenneighbors are in a same direction (e.g., all execution lanes shift left,all execution lanes shift right, etc.). Although it may be common for asame register to have its contents shifted out and replaced with contentthat is shifted in on a same cycle, the multiplexer arrangement 1203,1204 permits for different shift source and shift target registerswithin a same register file during a same cycle.

As depicted in FIG. 12 note that during a shift sequence an executionlane will shift content out from its register file 1202 to each of itsleft, right, top, and bottom neighbors. In conjunction with the sameshift sequence, the execution lane will also shift content into itsregister file from a particular one of its left, right, top, and bottomneighbors. Again, the shift out target and shift in source should beconsistent with a same shift direction for all execution lanes (e.g., ifthe shift out is to the right neighbor, the shift in should be from theleft neighbor).

Although in one embodiment the content of only one register is permittedto be shifted per execution lane per cycle, other embodiments may permitthe content of more than one register to be shifted in/out. For example,the content of two registers may be shifted out/in during a same cycleif a second instance of the multiplexer circuitry 1203, 1204 observed inFIG. 12 is incorporated into the design of FIG. 12. Of course, inembodiments where the content of only one register is permitted to beshifted per cycle, shifts from multiple registers may take place betweenmathematical operations by consuming more clock cycles for shiftsbetween mathematical operations (e.g., the contents of two registers maybe shifted between math ops by consuming two shift ops between the mathops).

If less than all the content of an execution lane's register files areshifted out during a shift sequence note that the content of the nonshifted out registers of each execution lane remain in place (do notshift). As such, any non-shifted content that is not replaced withshifted-in content persists local to the execution lane across theshifting cycle. The memory unit (“M”) observed in each execution lane isused to load/store data from/to the random access memory space that isassociated with the execution lane's row and/or column within theexecution lane array. Here, the M unit acts as a standard M unit in thatit is often used to load/store data that cannot be loaded/stored from/tothe execution lane's own register space. In various embodiments, theprimary operation of the M unit is to write data from a local registerinto memory, and, read data from memory and write it into a localregister.

With respect to the ISA opcodes supported by the ALU unit of thehardware execution lane 1201, in various embodiments, the mathematicalopcodes supported by the hardware ALU are integrally tied with (e.g.,substantially the same as) the mathematical opcodes supported by avirtual execution lane (e.g., ADD, SUB, MOV, MUL, MAD, ABS, DIV, SHL,SHR, MIN/MAX, SEL, AND, OR, XOR, NOT). As described just above, memoryaccess instructions can be executed by the execution lane 1201 tofetch/store data from/to their associated random access memory.Additionally the hardware execution lane 1201 supports shift operationinstructions (right, left, up, down) to shift data within thetwo-dimensional shift register structure. As described above, programcontrol instructions are largely executed by the scalar processor of thestencil processor.

3.0 Block Operations Implemented on Image Processor

a. Row/Column Sum Operation

FIGS. 13 and 14 a,b pertain to a row/column sum operation. Row/sumcolumn operations are particularly useful for statistics computation,noise suppression, and large scale down-sampling. Row sum and/or columnsum operations can be implemented on an image processor having atwo-dimensional execution lane array and corresponding two-dimensionalshift register array such as embodiments of the image processordescribed above in the preceding sections.

As observed in FIG. 13, a row sum operation adds all values in a samerow of an array and a column sum operation adds all values in a samecolumn of an array. Additionally, as depicted, with a row sum operationthe values of all rows can be simultaneously added within theirrespective rows. Likewise, with a column sum operation the values of allcolumns can be simultaneously added within their respective columns.Because of the versatility of the shift register array, however, summingacross all rows or columns is not a requirement. That is, less than allrows in an array may be simultaneously summed over or less that allcolumns in an array may be simultaneously summed over.

FIGS. 14a through 14d show an embodiment of a machine level operationfor implementing a row sum operation. For simplicity only a single rowis shown. The reader will understand that the operations depicted inFIGS. 14a through 14d can also be applied to a column. Additionally, forboth row or column operations, the sequence of FIGS. 14a through 14d canalso be simultaneously performed for multiple rows or columns in thearray. Additionally, the dimension of the row is only shown to be 8locations wide (whereas in actual implementations the execution lanearray and shift register array may be 16×16 or even larger).

In an implementation, as observed in FIG. 14a , the two-dimensionalshift register array is designed to support direct logical shiftsbetween opposite ends of the array 1401. That is, the shift register can“roll” or “loop” or “wrap” its content between a rightmost array columnand a leftmost array column when performing shifts along a row axis,and/or, roll or loop its content between a topmost array row and abottom most array row when performing shifts along a column axis.Additionally, in various embodiments, the shift register can supportmultiple register location hops in a single instruction (e.g., an opcodeand/or variable associated with a shift instruction specifies whetherthe shift amount is +/−1, +/−2, +/−3 or +/−4 register location placesalong horizontal and/or vertical axis). Shift distances that are notsupported in the hardware can be emulated by the compiler.

As observed in FIG. 14a , initially, the row is loaded with data valuesA0 through A7 in the respective R0 and R1 register locations of eachexecution lane. As observed in FIG. 14b , in a first iteration ofmachine operations, the R1 register space locations are then shiftedleft one location and the R1 and R0 contents of each execution lane aresummed with the resultant written back to R0 and R1. This produces afirst accumulated partial sum in R1 which, as will be made more clear inthe following discussion, acts as an accumulator for the overallsummation operation.

In a next iteration of machine operations, depicted in FIG. 14c , the R1register space locations are shifted left by two locations and the R1and R0 contents of each execution lane are summed. The resultant isagain kept in R0 and R1. Finally in a third iteration of machineoperations, depicted in FIG. 14d , the R1 register space locations areshifted left by four locations and the results written in either or bothof register locations R0 and R1. Thus, viewing the iterations of the sumoperation over FIGS. 14b, 14c, and 14d , note that the shift amountdoubles with each iteration and the complete result is present in alllanes after only three iterations (i.e., as of FIG. 14c ). In the caseof a 16 wide row, the shift amount would be eight locations for thefourth iteration and the operation would be complete after the fourthiteration.

b. Row/Column Prefix Sum Operation

FIGS. 15 and 16 a through 16 d pertain to a row/column prefix sumoperation that can also be executed on an image processor having atwo-dimensional execution lane array and a corresponding two-dimensionalshift register. Row/column prefix sum operations are particularly usefulfor integral images, accelerating box filters, and the computation ofaddresses for compaction operations. Referring to FIG. 15, forsimplicity, only a single row is shown. However, the operation can alsobe performed for columns. Also, although only one row is depicted, invarious implementations, as with the row/column sum operation discussedjust above, any number of rows (or columns) in the register array(including all rows/columns) can be simultaneously summed over.Additionally, the dimension of the row in FIG. 15 is only shown to be 8locations wide, whereas, in actual implementations the execution laneand shift register arrays may be 16×16 or even larger.

As observed in FIG. 15, the resultant of a row prefix operation for anylocation within a row is the sum of the values that lead up to thatlocation. Likewise, the value of a column prefix operation for anylocation within a column is the sum of the values that lead up to thatlocation.

FIGS. 16a through 16d shows an embodiment of a machine level operationfor a row prefix operation. As with the row sum operation discussed atlength in the preceding section, the row prefix operation employs theuse of a two dimensional shift register than can roll shifts betweenarray edge locations 1601.

As observed in FIG. 16a , a row is initially loaded with data values A0through A7 in the respective R0 register location of each executionlane. Also, a null (“0”) is loaded into the R2 register space of eachexecution lane.

In a first iteration of machine level operation, depicted in FIG. 16b ,the R0 register space locations are shifted right one location into thedestination location's R1 register space. A subsequent ADD operationadds the R0 content with either the R1 content or the R2 contentdepending on the location of the lane relative to the iteration count.Specifically, the first row location selects the null in R2 (and not theshifted content in R1) because its location (0) is equal to or less than2^(N)−1 where N is the iteration count (2⁰−1=0), adds the null to thecontent in R0 and stores the resultant back in R0. The first rowlocation, therefore will maintain a value of A0 in R0.

By contrast, each of the other row locations, because their location isgreater than 2^(N)−1, will select the shifted content in R1 (rather thanthe null value in R2), add it to the content in R0 and store theresultant in R0. Thus, each of the row locations other than the firstrow location will keep the sum of its original content and its leftmostneighbor in R0 whereas the first row location will simply keep only itsoriginal content in R0.

In a second iteration of machine level operations, depicted in FIG. 16c, the content of the R0 register space locations are shifted right twolocations into the destination's R1 register space. Thus, as with therow/column operations described immediately above, with each nextiteration of machine operations the shift amount doubles. As with thefirst iteration, a subsequent ADD operation adds the R0 content witheither the R1 content or the R2 content depending on the location of thelane relative to the current iteration count. In this case, the firstand second row locations select the null in R2 (and not the shiftedcontent in R1) because their location (0, 1) is less than or equal to2^(N)−1 (2 ¹-1=1). These lanes therefore add the null value to thecontent in R0 and stores the resultant back in R0. The first rowlocation, therefore will maintain its value of A0 in R0 and the secondrow location will maintain a value of A0+A1 in R0.

By contrast, each of the other row locations, because their location isgreater than the 2^(N)−1, will select the shifted content in R1 (ratherthan the null value in R2), add the content of R1 to the content in R0and store the resultant in R0. Thus, each of the row locations otherthan the first and second row locations will keep in R0 an accumulatedsum based on its original content and its total shifted in content.

In a third iteration of machine level operations, depicted in FIG. 16d ,the R0 register space locations are shifted right four locations intothe destination's R1 register space. Thus, again, with each nextiteration of machine operations the shift amount doubles. As with theearlier iterations, a subsequent ADD operation adds the R0 content witheither the R1 content or the R2 content depending on the location of thelane relative to the current iteration count. In this case, the firstthrough fourth row locations (0 through 3) will select the null in R2(and not the shifted content in R1) because their location is less thanor equal to 2^(N)−1 (2²−1=3). Each of these lanes will therefore add thenull value to the content in R0 and store the resultant back in R0. Thefirst row location, therefore will maintain its original value of A0 inR0, the second row location will maintain a value of A0+A1 in R0, thethird row location will maintain a value of A0+A1+A2 in R0 and thefourth row location will maintain a value of A0+A1+A2+A3 in R0.

By contrast, each of the other row locations, because their locationremains greater than 2^(N)−1, will select the shifted content in R1(rather than the null value in R2), add the content of R1 to the contentin R0 and store the resultant in R0. Thus, each of the row locationsother than the first, second and third row locations will keep anaccumulated sum based on its original content and its total shifted incontent.

After the third iteration, the prefix sum operation is complete. If therow were of dimension sixteen, only one more set of operations thatshift the R1 register contents by eight locations would be needed toaccumulate the summation unique to all 16 different locations in allsixteen execution lanes.

c. Row/Column Find Min Operation

FIGS. 17 and 18 a through 18 d pertain to a row/column find minimumoperation that can also be executed on an image processor having atwo-dimensional execution lane array and a corresponding two-dimensionalshift register. Row/column find min operations are particularly usefulfor statistics computations and block matching post-processing.

Referring to FIG. 17, for simplicity, only a single row is shown.However, in actual implementation, a column find minimum operation canbe implemented on a same processor that implements a row find minimumoperation. Additionally, the minimum for a row (or column) cansimultaneously be found for any number of rows (or columns) in theregister array (including up to all rows/columns). Additionally, thedimension of the row/column is only shown to be 8 locations wide,whereas, in actual implementations the execution lane and shift registerarrays may be 16×16 or even larger.

As observed in FIG. 17, the resultant of a row find minimum operationcorresponds to the smallest value amongst all values within a same rowand its location/position (also referred to as its index) in the row.Likewise, the resultant of a column find minimum operation correspondsto the smallest value amongst all values within a same column and itslocation/position within the column. As with the row sum and prefix sumoperations discussed at length in the preceding sections, the row/columnfind minimum operation employs the use of a two dimensional shiftregister than can roll shifts between array edge locations 1701.

FIGS. 18a through 18d show an embodiment of machine level operations fora row prefix operation. Initially, as observed in FIG. 18a , a row isloaded with data values A0 through A7 in the respective R0 registerlocation of each execution lane. Also, the index of each row location isloaded into the R1 register space of each execution lane.

In a first iteration of machine level operations, which are depicted inFIG. 18b , the content of the R0 and R1 register locations are shiftedone unit into the R2 and R3 register space of a neighboring executionlane's register space. The respective values of the R0 and R2 registersare then compared within each execution lane. The minimum value of thecomparison and its corresponding index are stored into the R0 and R1register space. That is, if the R0 value is less than the R2 value, theR0 and R1 registers maintain their original content. Whereas, if the R2value is less than the R0 value, the R2 value is written into R0 and theR3 value is written into R1. This has the effect of keeping the minimumvalue of the comparison in R0 and its index in R1.

In a second iteration of machine level operations, which are depicted inFIG. 18c , the content of the R0 and R1 register locations are shiftedtwo units into the R2 and R3 register space of a downstream executionlane. Thus, once again, the shift amount doubles with a next iteration.The respective values of the R0 and R2 registers are then comparedwithin each execution lane. The minimum value of the comparison and itscorresponding index are stored into the R0 and R1 register space. Thishas the effect of keeping the minimum value observed from bothcomparisons that have been performed in each execution lane in R0 andits index in R1.

In a third iteration of machine level operations, observed in FIG. 18d ,the content of the R0 and R1 register locations are shifted four unitsinto the R2 and R3 register space of a downstream execution lane. Therespective values of the R0 and R2 registers are then compared withineach execution lane. The minimum value of the comparison and itscorresponding index are stored into the R0 and R1 register space. Thishas the effect of keeping the minimum value observed from all threecomparisons that have been performed in each execution lane in R0 andits index in R1.

After the third iteration, the find minimum operation is complete aseach execution lane will have the minimum value of the entire row in itsR0 register space and its corresponding index in its R1 register space(the row location that was originally provided with the minimum valuewill find its own row location identified in its R1 register space). Ifthe row were of dimension sixteen, only one more set of operations basedon a shift of the R0 and R1 register contents downstream in the shiftregister by eight locations would be needed to provide the minimum ofall sixteen different locations in all sixteen execution lanes.

Note that a find maximum operation could also be implemented using thesame principles described above except that the core math operationincludes finding the maximum rather than finding the minimum.

d. Matrix Multiply

FIGS. 19a,b and 20 pertain to a matrix multiply. A matrix multiply isparticularly useful for discrete fourier or cosine transforms (which arecommon primitives in compression and filtering) and to express largermatrix/multiply operations (which are commonly used in imagerecognition). A matrix multiply of two matrices A and B is performed bysumming, for each matrix coordinate location in the resultant, productsof the elements in the row of the coordinate location and theircorresponding elements in the column of the coordinate location. FIG.19b shows the resultant matrix X for the matrix multiple of matrices Aand B in FIG. 19a . Here, associated partial product terms of matrices Aand B for two coordinate locations 1901, 1902 in the resultant matrix Care specially shown.

In particular, for instance, the resultant product for coordinatelocation c12 in the resultant matrix C of FIG. 19b is

(a11*b11)+(a12*b21)+(a13*b31)+(a14*b41)

which corresponds to the elements of row 1901 in matrix A beingmultiplied with the corresponding elements of column 1902 in matrix B inFIG. 19 a.

Likewise, the resultant product for coordinate location c22 in resultantmatrix C of FIG. 19b is

(a21*b12)+(a22*b22)+(a23*b32)+(a24*b42)

which corresponds to the elements of row 1903 in matrix A beingmultiplied with the corresponding elements of column 1902 in matrix B inFIG. 19a . As can seen from these two examples, the resultant for anycoordinate location x,y in the resultant matrix C can be expressed as:

Σ_(k=1 to 4)(a _(x,k))*(b _(k,y)).

FIGS. 20a through 20e show an embodiment of a matrix multiply operationthat uses a two dimensional execution lane array and the unique shiftingadvantages of a corresponding two dimensional shift register array.

As observed in FIG. 20a , initially, two matrices A and B are loadedinto the two dimensional shift register array. For example, the valuesof matrix A may be loaded into the R0 register space of the twodimensional shift register and the values of matrix B may be loaded intothe R1 register space of the two dimensional shift register array suchthat each matrix coordinate corresponds to a different execution lane'sassociated register space. Again, for illustrative ease, 4×4 matricesare depicted although in actual implementations larger matrices can bemultiplied with a corresponding, larger dimensioned shift registerarray.

As observed in FIG. 20b , a rotational shearing algorithm shift isapplied to both matrices with a row-wise rotational shearing algorithmshift sequence being applied to matrix A and a column-wise rotationalshearing algorithm shift sequence being applied to matrix B. As is knownin the art, a rotational shearing algorithm increases shift amount byN−1 where N is the position in the matrix.

Thus, as observed in FIG. 20b , the first row of matrix A is not shiftedat all, the second row of matrix A is shifted one unit, the third row ofmatrix A is shifted two units and the fourth row of matrix A is shiftedthree units. Similarly, the first column of matrix B is not shifted atall, the second column of matrix B is shifted one unit, the third columnof matrix B is shifted two units and the fourth column of matrix B isshifted three units. Here, the two dimensional shift register array isunderstood to be able to roll elements at array edges for both roworiented shifts and column oriented shifts.

Note that, owing to the versatile nature of the two dimensional shiftregister array and the corresponding execution lane array where therespective shift instruction executed by each execution lane can specifydifferent input operand data, the two dimensional shift register arrayis able to shift different rows by different horizontal shift amountsand shift different columns by different vertical shift amounts whilesimultaneously executing the shift instructions across all executionlanes for a same matrix (in various embodiments, a same horizontal shiftamount must be specified for lanes in a same row and a same verticalshift amount must be specified for lanes in a same column). Thus,conceivably, the shearing of both the A and B matrices can be completedin as few as two cycles (i.e., all shifts for one matrix are performedin one cycle assuming the shift register can implement multiple hopshifts in a single cycle).

With the data in matrices A and B being realigned from the shearingalgorithms, as observed in FIG. 20b , a multiply operation is performedwhere each execution lane multiplies the A and B values in itscorresponding two dimensional shift register space. Here, recall that Avalues are, e.g., kept in R0 space and B values are kept in R1 space.The resultant of the multiplication is stored in local R2 space. Nullvalues may be loaded as an initial condition into R3 space and theresultant of the multiplication in R2 is added to the contents of R3.The resultant of the summation is stored back in R3. As will be apparentin the teachings that follow, R3 takes on the roll of accumulator thataccumulates the summation of partial product terms over the course thematrix multiply operation.

For ease of understanding, FIG. 20b explicitly shows the contents in theresultant R3 space after the first iteration for coordinate locationsc11 and c22 in the resultant matrix C originally depicted in FIG. 19b .Here, after the first iteration of FIG. 20b , the R3 register space atlocation C11 contains the partial product term a11*b11 and the R3register space at location C22 contains the partial product term(a21*b12).

As observed in FIG. 20c , upon a next iteration, the R0 registerscontaining matrix A data are then horizontally shifted one unit and theR1 registers containing matrix B data are vertically shifted one unit.The mathematical operations described just above with respect to FIG.20b are then repeated. Here, however, the R3 register space of each laneinitially contains the first iteration's partial product term (e.g.,a11*b11 in R3 of location c11 and a21*b12 in R3 of location c22). Assuch, at the end of the iteration, register R3 will contain theaccumulated sum of both partial products that have so far beencalculated. That is, R3 in location c11 will have the sum(a11*b11)+(a12*b21) and R3 in location c22 will have the sum(a21*b12)+(a22*b22).

As observed in FIGS. 20d and 20e after two more iterations of a singleunit shift for both matrices followed by a multiply-add, the matrixmultiply will be complete with each register array location having thecorrect summation of partial products in its local R3 register space.

e. Two Dimensional Discrete Fourier Transform (2D DFT)

FIG. 21 depicts a two dimensional DFT (2D DFT). A 2D DFT is particularlyuseful for noise reduction and accelerating convolutions. As observed inFIG. 21, a 2D DFT can be expressed as the summation over two dimensionalspace of the product of two complex terms 2101, 2102. A first of thecomplex terms 2101 corresponds to a phasor whose magnitude and phase isa function of time and frequency. In implementation, the first complexterm 2101 is expressly calculated as a first matrix of coefficients. Asecond of the complex terms 2102 corresponds to the signal that is beingtransformed from the spatial domain to the frequency domain.

For simplicity, FIG. 21 represents the first complex term 2101 asRe1+jlm1 and represents the second complex 2102 term as Re2+jlm2. As isknown in the art, the real part of (Re1+jlm1)*(Re2+jlm2) can beexpressed as (Re1*Re2)−(Im1*Im2) while the imaginary part can beexpressed as j((Re1*Im2)+(Re2*Im1)). The summations of the 2D DFT over2D space, just like the matrix multiply discussed at length immediatelyabove, add the products of elements in a row of a coordinate location bycorresponding elements in the column of the coordinate location.

Thus, the real part of the DFT resultant can be calculated by performinga matrix multiply on an array of Re1 values and an array of Re2 valuesand subtracting from the resultant array the result of a matrix multiplyon an array of Im1 values and Im2 values. Similarly, the imaginary partof the DFT resultant can be calculated by performing a matrix multiplyon an array of Re1 values and an array of Im2 values and adding theresultant array to the result of a matrix multiply on an array of Re2values and Im1 values.

FIG. 22a shows machine operations for calculating the real part of theDFT. As observed in FIG. 22a , an array of Re1 values are loaded intothe R0 register space of the two-dimensional shift register array, anarray of Re2 values are loaded into the R1 register space of thetwo-dimensional shift register array, an array of Im1 values are loadedinto the R2 register space of the two-dimensional shift register array,and an array of Im2 values are loaded into the R3 register space of thetwo-dimensional shift register array. As observed in FIG. 22b , arotational shearing algorithm is then applied to each of the arrayvalues with the Re1 and the Im1 values being sheared horizontally andthe Re2 and Im2 values being sheared vertically.

As observed in FIG. 22c , an Re1*Re2 matrix multiply and an Im1*Im2matrix multiply are then performed with the resultants being kept in theR0 and R2 register space, respectively. The content of the R2 registerspace is then subtracted from the R0 register spacing with the resultantof the subtraction leaving the real part of the DFT transform in the R0register space as observed in FIG. 22 d.

In an embodiment, the real part resultant in the R0 register space ismoved to R4 register space (if it exists) or written out to local memorythat is coupled to the shift register array. Then, the original Re1 andIm1 values are re-written back into the R0 and R1 register space (e.g.,from the same local memory) and horizontally sheared so that theregister content of FIG. 22a is recreated in the two-dimensional shiftregister array.

An Re1*Im2 matrix multiply and an Re2*Im1 matrix multiply are thenperformed with the resultants being kept in the R0 and R2 registerspace, respectively. That is, a matrix multiply is performed on thecontents of R0 and R3 with the resultant written back to R0, and, amatrix multiply is performed on the contents of R2 and R1 the contentsbeing written into R2. The resultant matrices in R0 and R2 are shown inFIG. 22e . The content of the R0 register space is then added to thecontent of the R2 register spacing and written back to R0. This leavesthe imaginary part of the DFT transform in the R0 register space asdepicted in FIG. 22 f.

f. FFT Butterfly

As is known in the art, a fast fourier transform (FFT) is a faster, lesscomputationally intensive approach to a DFT. FFTs rely on specialefficient algorithms to rapidly convert time or space domain data intofrequency domain data. A critical component of such algorithms is abutterfly algorithm. An exemplary butterfly algorithm is depicted inFIG. 23. Here, a butterfly operation is defined by a stage where thespecific stage determines an amount of swapping that transpires betweenelements of a same row or column. As is known in the art, a complete FFTincludes performing mathematical operations on the swapped content ofmultiple, different stage butterfly operations in between the butterflyoperations.

FIG. 23 shows each of 1, 2, and 4 stage butterfly operations. In thecase of the 1 stage butterfly, neighboring elements are swapped. In thecase of the 2 stage butterfly, neighboring pairs of elements areswapped. In the case of the 4 stage butterfly, groups of 4 neighboringelements are swapped. In the case of a two dimensional FFT, elements ina first array of signal data are swapped according to each of multiplebutterfly stages with mathematical operations being performed on theswapped signal data elements.

FIG. 24a shows machine level shift operations that can be used to effecta 1 stage 1 butterfly across an array of signal data that is stored intwo dimensional R0 register space. For simplicity only one row is shown.It is pertinent to recognize that multiple (e.g., all) rows or columnsof an array in a two dimensional shift register may be simultaneouslyprocessed in accordance with the particular row that is observed.

Here, the shift register is initially loaded with A0 through A7 acrosseach of its rows in its R0 register space. The shift register thenshifts the R0 register content one unit to the right and each executionlane stores the data that has been just been shifted into its locationin its R1 register space. Then, the shift register shifts the R0register content two units to the left (the resultant of which islabeled R0′). Each execution lane then executes a selection operation inwhich either its local R0 content or its local R1 content is stored inR0 (i.e., if R0 is selected, the content of R0 remains unchanged)depending on the location of the lane. In the particular embodiment ofFIG. 24a , even lanes select R0 while odd lanes select R1. After theselection, the correctly swapped values are in the R0 register space ofeach execution lane (labeled as R0″).

FIG. 24b and FIG. 24c depict 2 stage and 4 stage butterfly operations.Processing is similar to the 1 stage butterfly operation described justabove, except that in the case of the 2 stage butterfly the shiftregister array shifts the R0 register content two units to the right andthen four units to the left. Every other even lane and its rightmostneighbor select from one of R1 and R0″ whereas the other even lanes antheir rightmost neighbor select from the other of R1 and R0″. In thecase of the 4 stage butterfly, depicted in FIG. 25c , the shift registerarray shifts the contents of R0 four units to the right and then selectsall values as they reside in R0 (labeled R0′).

q. Block Match

FIG. 25 shows a depiction of block matching. Block matching isparticularly useful for motion estimation (e.g., for video compression),image stabilization, and image fusion algorithms (e.g., exposure fusion,and temporal noise fusion). Here, a specific feature in a first base(e.g., previous) image looked for in an alternative (e.g., later) image.In the example of FIG. 26, the block ABCD that is present in the baseimage needs to be found in the alternative image.

FIGS. 26a through 26d shows a method for performing block matching on animage processor having a two dimensional execution lane array and a twodimensional shift register array. Here, the pixels of the alternativeimage are kept in the R0 register space of the two dimensional shiftregister. A first pixel of the feature in the base image that is beinglooked for (e.g., “A”) is broadcast to all execution lanes and anabsolute difference is taken on the content in the R0 register space andthe value “A” and the resultant is stored in R1 (for simplicity it isassumed that no other pixels in the alternative image have any of thelooked for feature's values (A, B, C, D). If a pixel value in thealternative image matches (or approximately matches) the broadcast pixelvalue A then the resultant in R1 should be at (or near) zero. All otherresultants in R1 should be substantially non zero.

Referring to FIG. 26b , the alternative image is then shifted one unitin the two-dimensional shift register, a next pixel value “B” in thefeature being looked for is broadcast to all execution lanes and theabsolute difference is again taken and stored in R1. Here, theparticular execution lane array location 2601 that has had twoconsecutive pixel matches should have the lowest resultant value in R1.This particular execution lane location is the location where theparticular order of pixel values that are being broadcast aligns withthe particular scanning/shifting motion of the alternative image in R0of the shift register array.

As observed in FIGS. 26c and 26d , the process continues with each nextiteration broadcasting a next pixel value and shifting the alternativeimage data in a particular scan order. After a number of iterationssufficient to broadcast all sought for image pixels and tocorrespondingly shift the alternative image in R0 over an area thatcorresponds to the size of the looked for image, ideally, only onelocation 2601 in the execution lane array will have experienced a matchon every iteration cycle. As such, this particular array location 2601should be able to maintain a zero or near zero value in its R1 registerspace (or at least a smaller value than the other execution lanes) afterall iterations have been completed.

A findmin operation as discussed above is executed on the R1 registerspace across all rows in the array. The lowest corresponding value ineach row will then be kept at each location of its row. A findminoperation is then executed on the R1 register space across all columnsin the array. The resultant should identify the pixel that matched thebase image on every iteration which, in turn, can be used to identifythe precise location of the looked for image in the alternative array.

4.0 Construction of Low Level Program Code

FIG. 27 shows a pre-runtime development environment in which aprogrammer designs a high level image processing function and theapplication development environment (which may include the virtual ISAenvironment discussed at length above with respect to FIGS. 1 through 6)provides for any/all of the aforementioned special operations so thatthe developer does not have the write them from scratch.

Here, the developer may specifically call out any of the operationsdiscussed at length above and/or the development environmentautomatically provides them from a library 2701 in response.Alternatively or in combination, the developer's need for suchoperations may be implied or deduced (such as a matrix multiply in thecase of a 2D DFT) and the development environment automatically insertsprogram code from the library 2701 that performs these functions (e.g.,as part of a compilation process).

Thus, the program code that performs the above described operations oralternate embodiments thereof may be expressed in higher level (e.g.,virtual ISA) program code or lower level object code. In variousembodiments, the higher level virtual ISA code may specify data valuesto be operated upon as memory reads having x,y address coordinates,while, the object code may instead comprehend these data accesses astwo-dimensional shift register operations (such as any of the shiftoperations described above or similar embodiments). A compiler mayconvert the x,y reads in the development environment into correspondingshifts of the two dimensional shift register that are specified objectcode (e.g., a read in the development environment having x,y coordinates(+2, +2) may be realized in object code as a shift to the left twospaces and a shift down of two spaces). Depending on environment, thedeveloper may have visibility into both of these levels (or, e.g., justthe higher VISA level). In still yet other embodiments, such prewrittenroutines may be invoked during runtime (e.g., by a just-in-timecompiler) rather than pre-runtime.

5.0 Concluding Statements

From the preceding sections is pertinent to recognize that the virtualenvironment described above in Section 1.0 may be instantiated on acomputer system. Likewise an image processor as described above inSection 2.0 may be embodied in hardware on a computer system (e.g., aspart of a handheld device's System on Chip (SOC) that processes datafrom the handheld device's camera).

It is pertinent to point out that the various image processorarchitecture features described above are not necessarily limited toimage processing in the traditional sense and therefore may be appliedto other applications that may (or may not) cause the image processor tobe re-characterized. For example, if any of the various image processorarchitecture features described above were to be used in the creationand/or generation and/or rendering of animation as opposed to theprocessing of actual camera images, the image processor may becharacterized as a graphics processing unit. Additionally, the imageprocessor architectural features described above may be applied to othertechnical applications such as video processing, vision processing,image recognition and/or machine learning. Applied in this manner, theimage processor may be integrated with (e.g., as a co-processor to) amore general purpose processor (e.g., that is or is part of a CPU ofcomputing system), or, may be a stand alone processor within a computingsystem.

The hardware design embodiments discussed above may be embodied within asemiconductor chip and/or as a description of a circuit design foreventual targeting toward a semiconductor manufacturing process. In thecase of the later, such circuit descriptions may take of the form of a(e.g., VHDL or Verilog) register transfer level (RTL) circuitdescription, a gate level circuit description, a transistor levelcircuit description or mask description or various combinations thereof.Circuit descriptions are typically embodied on a computer readablestorage medium (such as a CD-ROM or other type of storage technology).

From the preceding sections is pertinent to recognize that an imageprocessor as described above may be embodied in hardware on a computersystem (e.g., as part of a handheld device's System on Chip (SOC) thatprocesses data from the handheld device's camera). In cases where theimage processor is embodied as a hardware circuit, note that the imagedata that is processed by the image processor may be received directlyfrom a camera. Here, the image processor may be part of a discretecamera, or, part of a computing system having an integrated camera. Inthe case of the later the image data may be received directly from thecamera or from the computing system's system memory (e.g., the camerasends its image data to system memory rather than the image processor).Note also that many of the features described in the preceding sectionsmay be applicable to a graphics processor unit (which rendersanimation).

FIG. 28 provides an exemplary depiction of a computing system. Many ofthe components of the computing system described below are applicable toa computing system having an integrated camera and associated imageprocessor (e.g., a handheld device such as a smartphone or tabletcomputer). Those of ordinary skill will be able to easily delineatebetween the two.

As observed in FIG. 28, the basic computing system may include a centralprocessing unit 2801 (which may include, e.g., a plurality of generalpurpose processing cores 2815_1 through 2815_N and a main memorycontroller 2817 disposed on a multi-core processor or applicationsprocessor), system memory 2802, a display 2803 (e.g., touchscreen,flat-panel), a local wired point-to-point link (e.g., USB) interface2804, various network I/O functions 2805 (such as an Ethernet interfaceand/or cellular modem subsystem), a wireless local area network (e.g.,WiFi) interface 2806, a wireless point-to-point link (e.g., Bluetooth)interface 2807 and a Global Positioning System interface 2808, varioussensors 2809_1 through 2809_N, one or more cameras 2810, a battery 2811,a power management control unit 2824, a speaker and microphone 2813 andan audio coder/decoder 2814.

An applications processor or multi-core processor 2850 may include oneor more general purpose processing cores 2815 within its CPU 2801, oneor more graphical processing units 2816, a memory management function2817 (e.g., a memory controller), an I/O control function 2818 and animage processing unit 2819. The general purpose processing cores 2815typically execute the operating system and application software of thecomputing system. The graphics processing units 2816 typically executegraphics intensive functions to, e.g., generate graphics informationthat is presented on the display 2803. The memory control function 2817interfaces with the system memory 2802 to write/read data to/from systemmemory 2802. The power management control unit 2824 generally controlsthe power consumption of the system 2800.

The image processing unit 2819 may be implemented according to any ofthe image processing unit embodiments described at length above in thepreceding sections. Alternatively or in combination, the IPU 2819 may becoupled to either or both of the GPU 2816 and CPU 2801 as a co-processorthereof. Additionally, in various embodiments, the GPU 2816 may beimplemented with any of the image processor features described at lengthabove.

Each of the touchscreen display 2803, the communication interfaces2804-2807, the GPS interface 2808, the sensors 2809, the camera 2810,and the speaker/microphone codec 2813, 2814 all can be viewed as variousforms of I/O (input and/or output) relative to the overall computingsystem including, where appropriate, an integrated peripheral device aswell (e.g., the one or more cameras 2810). Depending on implementation,various ones of these I/O components may be integrated on theapplications processor/multi-core processor 2850 or may be located offthe die or outside the package of the applications processor/multi-coreprocessor 2850.

In an embodiment one or more cameras 2810 includes a depth cameracapable of measuring depth between the camera and an object in its fieldof view. Application software, operating system software, device driversoftware and/or firmware executing on a general purpose CPU core (orother functional block having an instruction execution pipeline toexecute program code) of an applications processor or other processormay perform any of the functions described above.

Embodiments of the invention may include various processes as set forthabove. The processes may be embodied in machine-executable instructions.The instructions can be used to cause a general-purpose orspecial-purpose processor to perform certain processes. Alternatively,these processes may be performed by specific hardware components thatcontain hardwired logic for performing the processes, or by anycombination of programmed computer components and custom hardwarecomponents.

Elements of the present invention may also be provided as amachine-readable medium for storing the machine-executable instructions.The machine-readable medium may include, but is not limited to, floppydiskettes, optical disks, CD-ROMs, and magneto-optical disks, FLASHmemory, ROMs, RAMs, EPROMs, EEPROMs, magnetic or optical cards,propagation media or other type of media/machine-readable mediumsuitable for storing electronic instructions. For example, the elementsmay be downloaded as a computer program transferred from a remotecomputer (e.g., a server) to a requesting computer (e.g., a client) byway of data signals embodied in a carrier wave or other propagationmedium via a communication link (e.g., a modem or network connection).

In the foregoing specification, specific example embodiments have beendescribed. It will, however, be evident that various modifications andchanges may be made thereto without departing from the broader spiritand scope of the invention as set forth in the appended claims. Thespecification and drawings are, accordingly, to be regarded in anillustrative rather than a restrictive sense.

1. A processor comprising: a two-dimensional array of processingelements; and multiple shift-register planes, each shift-register planecomprising a separate two-dimensional shift-register array, wherein eachshift register of each shift-register array is dedicated to one of theprocessing elements, wherein the processor is configured to executeinstructions to perform a Fast Fourier Transform (FFT) operation on afirst matrix stored in a first shift-register plane, wherein theinstructions cause the processor to perform operations comprising:performing i-stage butterfly operations on each row in the firstshift-register plane for each of a plurality of stages in which thevalue of i starts at 1 and increases by powers of 2 until a maximumvalue of i is reached, including performing, for each stage, operationscomprising: shifting data in the first shift-register plane i units in afirst direction, based on determining that i is less than a maximumvalue, copying the shifted data to a second shift-register plane,shifting data in the first shift-register plane i×2 units in a seconddirection that is opposite to the first direction, based on determiningthat i is less than a maximum value, performing, by each processingelement, a selection operation that stores, in the first shift-registerplane, either data in the first shift-register plane or data in thesecond shift-register plane, and performing one or more FFT operationson data in the first shift-register plane.
 2. The processor of claim 1,wherein performing the i-stage butterfly operations comprises:performing a 1-stage butterfly operation on each row in the firstshift-register plane, including: shifting data in the firstshift-register plane one unit in a first direction, copying the shifteddata to a second shift-register plane, shifting data in the firstshift-register plane two units in a second direction that is opposite tothe first direction, performing, by each processing element, a selectionoperation that stores, in the first shift-register plane, either data inthe first shift-register plane or data in the second shift-registerplane, and performing one or more FFT operations on data in the firstshift-register plane; performing a 2-stage butterfly operation on eachrow in the first shift-register plane, including: shifting data in thefirst shift-register plane two units in the first direction, copying theshifted data to the second shift-register plane, shifting data in thefirst shift-register plane four units in the second direction,performing, by each processing element, a selection operation thatstores, in the first shift-register plane, either data in the firstshift-register plane or data in the second shift-register plane, andperforming one or more FFT operations on data in the firstshift-register plane; and performing a 4-stage butterfly operation oneach row in the first shift-register plane, including: shifting data inthe first shift-register plane four units in the first direction, andperforming one or more FFT operations on data in the firstshift-register plane.
 3. A method performed by a processor having atwo-dimensional array of processing elements and multiple shift-registerplanes, wherein the shift-register planes each comprise a separatetwo-dimensional shift-register array, wherein each register of eachshift-register array is dedicated to one processing element in thetwo-dimensional array of processing elements, wherein the method causesthe processor to perform a Fast Fourier Transform (FFT) operation on afirst matrix stored in a first shift-register plane, the methodcomprising: performing i-stage butterfly operations on each row in thefirst shift-register plane for each of a plurality of stages in whichthe value of i starts at 1 and increases by powers of 2 until a maximumvalue of i is reached, including performing, for each stage, operationscomprising: shifting data in the first shift-register plane i units in afirst direction, based on determining that i is less than a maximumvalue, copying the shifted data to a second shift-register plane,shifting data in the first shift-register plane i×2 units in a seconddirection that is opposite to the first direction, based on determiningthat i is less than a maximum value, performing, by each processingelement, a selection operation that stores, in the first shift-registerplane, either data in the first shift-register plane or data in thesecond shift-register plane, and performing one or more FFT operationson data in the first shift-register plane.
 4. The method of claim 3,wherein performing the i-stage butterfly operations comprises:performing a 1-stage butterfly operation on each row in the firstshift-register plane, including: shifting data in the firstshift-register plane one unit in a first direction, copying the shifteddata to a second shift-register plane, shifting data in the firstshift-register plane two units in a second direction that is opposite tothe first direction, performing, by each processing element, a selectionoperation that stores, in the first shift-register plane, either data inthe first shift-register plane or data in the second shift-registerplane, and performing one or more FFT operations on data in the firstshift-register plane; performing a 2-stage butterfly operation on eachrow in the first shift-register plane, including: shifting data in thefirst shift-register plane two units in the first direction, copying theshifted data to the second shift-register plane, shifting data in thefirst shift-register plane four units in the second direction,performing, by each processing element, a selection operation thatstores, in the first shift-register plane, either data in the firstshift-register plane or data in the second shift-register plane, andperforming one or more FFT operations on data in the firstshift-register plane; and performing a 4-stage butterfly operation oneach row in the first shift-register plane, including: shifting data inthe first shift-register plane four units in the first direction, andperforming one or more FFT operations on data in the firstshift-register plane.
 5. A computer program product encoded on one ormore non-transitory computer storage media, comprising instructions thatwhen executed by a processor comprising: a two-dimensional array ofprocessing elements, and multiple shift-register planes, eachshift-register plane comprising a separate two-dimensionalshift-register array, wherein each shift register of each shift-registerarray is dedicated to one of the processing elements, cause theprocessor to perform a Fast Fourier Transform (FFT) operation on a firstmatrix stored in a first shift-register plane, the FFT operationcomprising: performing i-stage butterfly operations on each row in thefirst shift-register plane for each of a plurality of stages in whichthe value of i starts at 1 and increases by powers of 2 until a maximumvalue of i is reached, including performing, for each stage, operationscomprising: shifting data in the first shift-register plane i units in afirst direction, based on determining that i is less than a maximumvalue, copying the shifted data to a second shift-register plane,shifting data in the first shift-register plane i×2 units in a seconddirection that is opposite to the first direction, based on determiningthat i is less than a maximum value, performing, by each processingelement, a selection operation that stores, in the first shift-registerplane, either data in the first shift-register plane or data in thesecond shift-register plane, and performing one or more FFT operationson data in the first shift-register plane.
 6. The computer programproduct of claim 5, wherein performing the i-stage butterfly operationscomprises: performing a 1-stage butterfly operation on each row in thefirst shift-register plane, including: shifting data in the firstshift-register plane one unit in a first direction, copying the shifteddata to a second shift-register plane, shifting data in the firstshift-register plane two units in a second direction that is opposite tothe first direction, performing, by each processing element, a selectionoperation that stores, in the first shift-register plane, either data inthe first shift-register plane or data in the second shift-registerplane, and performing one or more FFT operations on data in the firstshift-register plane; performing a 2-stage butterfly operation on eachrow in the first shift-register plane, including: shifting data in thefirst shift-register plane two units in the first direction, copying theshifted data to the second shift-register plane, shifting data in thefirst shift-register plane four units in the second direction,performing, by each processing element, a selection operation thatstores, in the first shift-register plane, either data in the firstshift-register plane or data in the second shift-register plane, andperforming one or more FFT operations on data in the firstshift-register plane; and performing a 4-stage butterfly operation oneach row in the first shift-register plane, including: shifting data inthe first shift-register plane four units in the first direction, andperforming one or more FFT operations on data in the firstshift-register plane.